___ Ca + ____ AlCl₃ -----> ___ CaCl₂ + ___ Al
To answer this question we will list all the elements that we have on each side of the equation and then we will try to balance the amount of them.
___ Ca + ____ AlCl₃ -----> ___ CaCl₂ + ___ Al
Ca: 1 -------> Ca: 1
Al: 1 ------> Al: 1
Cl: 3 -------> Cl: 2
Ca and Al are already balanced, Cl is the one that we have to balance
To balance the Cl we have to "cross multiply". That will result in:
___ Ca + ____ AlCl₃ -----> ___ CaCl₂ + ___ Al
Ca: 1 -------> Ca: 1
Al: 1 ------> Al: 1
Cl: 3 * 2 = 6 -------> Cl: 2 * 3 = 6
And we put those numbers as the coefficients of the compounds:
___ Ca + 2 AlCl₃ -----> 3 CaCl₂ + ___ Al
Now that we changed the coefficients, we changed the amount of the elements, so we will have to calculate them again:
___ Ca + 2 AlCl₃ -----> 3 CaCl₂ + ___ Al
Ca: 1 -------> Ca: 3
Al: 2 ------> Al: 1
Cl: 6 -------> Cl: 6
There the amount of Al changed on the left and the amount of Ca changed on the right. So we balanced the Cl but we unbalanced the Al, and the Ca.
If we want to balance the Ca, we only have to multiply by 3 on the left side:
___ Ca + 2 AlCl₃ -----> 3 CaCl₂ + ___ Al
Ca: 1 * 3 = 3 -------> Ca: 3 * 1 = 3
Al: 2 ------> Al: 1
Cl: 6 -------> Cl: 6
So the coefficient for Ca on the left is going to be 3:
3 Ca + 2 AlCl₃ -----> 3 CaCl₂ + ___ Al
And finally we have to do something similar with Aluminum that is the last element that we have to balance to find our answer:
3 Ca + 2 AlCl₃ -----> 3 CaCl₂ + ___ Al
Ca: 3 -------> Ca: 3
Al: 2 * 1 = 2 ------> Al: 1 * 2 = 2
Cl: 6 -----> Cl: 6
The last coefficient of our reaction, and the answer to our problem is
3 Ca + 2 AlCl₃ -----> 3 CaCl₂ + 2 Al
So, our reaction is now balanced and the coefficient in front of the Al is 2